Compute some properties of compound interest rates

by RoRi

January 13, 2016

Consider a bank account which starts with $P$ dollars and pays an interest rate $r$ per year, compounding $m$ times per year.

Prove that the balance in the bank account at the end of $n$ years is
$P \left( 1 + \frac{r}{m} \right)^{mn}.$

For fixed values of $r$ and $n$ , the balance at the end of $n$ years as $m \to +\infty$ is given by

$\lim_{m \to +\infty} P \left( 1 + \frac{r}{m} \right)^{mn} = Pe^{rn}.$

We say that money grows at the annual rate $r$ with continuous compounding if the amount of money after $t$ years is denoted by $f(t)$ is given by

$f(t) = f(0)e^{rt}.$

Give an approximate length of time for the money in a bank account to double if $r = .06$ and compounds:

Incomplete. Sorry, I’ll try to get back to this soon(ish).

Stumbling Robot